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32nd IEEE Signal Processing and Communications Applications Conference (SIU)

作者： Oztemiz, Furkan Yakut, Selman Inonu Univ Engn Fac Malatya Turkiye

ISBN: (纸本)9798350388978;9798350388961

centrality is a frequently used metric in graph theory that identifies the dominance values of nodes. In this study, the malatya centrality algorithm, which approaches graph centrality from a new perspective, has been proposed. To calculate the centrality of a node in the graph, the ratio of the node's degree to the degrees of its neighboring nodes was computed and these ratios were summed. The results of the proposed algorithm were compared with established centrality algorithms in the literature and tested on well-known social networks such as Zachary's karate club, the dolphin social network, and the zebra network. The tests and analyses conducted demonstrate that the malatya centrality algorithm is an effective and successful centrality algorithm.

关键词： Betweenness Closeness Eigenvector malatya centrality malatya centrality algorithm Pagerank

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A robust and efficient algorithm for graph coloring problem based on malatya centrality and sequent independent sets

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EGYPTIAN INFORMATICS JOURNAL 2025年 30卷

作者： Yakut, Selman Inonu Univ Fac Engn Dept Biomed Engn TR-44000 Malatya Turkiye

The Graph Coloring Problem (GCP) is an NP-hard problem that aims to color the vertices of a graph using the minimum number of distinct colors, ensuring that adjacent vertices do not share the same color. GCP is widely applied in real-world scenarios and graph theory problems. Despite numerous studies on solving GCP, existing methods face limitations, often performing well on specific graph types but failing to deliver efficient solutions across diverse structures. This study introduces the malatya Sequent Independent Set Coloring algorithm as an effective solution for GCP. The algorithm utilizes the malatya centrality algorithm to compute malatya centrality (MC) values for graph vertices, where an MC value is defined as the sum of the ratios of a vertex's degree to its neighbors' degrees. The algorithm selects the vertex with the lowest MC value, adds it to an independent set, and removes it along with its neighbors and edges. This process repeats until the first sequent independent set is identified. The removed set is then excluded from the original graph, and the process continues on the remaining structure to determine additional sequent independent sets, ensuring that each set corresponds to a single color group in GCP. The algorithm was tested on social network graphs, random graphs, and benchmark datasets, supported by mathematical analyses and proofs. The results confirm that the algorithm provides efficient, polynomial-time solutions for GCP and maintains high performance across various graph types, independent of constraints.

关键词： Graph coloring problem Chromatic numbers malatya centrality algorithm malatya sequent independent set coloring algorithm Independent sets

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A new robust approach to solve minimum vertex cover problem: malatya vertex-cover algorithm

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JOURNAL OF SUPERCOMPUTING 2023年第17期79卷 19746-19769页

作者： Yakut, Selman Oztemiz, Furkan Karci, Ali Inonu Univ Software Engn Dept Malatya Turkiye

The minimum vertex-cover problem (MVCP) is an NP-complete optimization problem widely used in areas such as graph theory, social network, security and transportation, etc. Different approaches and algorithms have been proposed in the literature to solve this problem, since MVCP is an optimization problem, the solutions developed for this problem could be more intuitive and give results under certain constraints. In addition, the proposed solution methods for this problem could be more effective, and the determined solution sets change in each iteration. The algorithms/methods developed for solving MVCP are mostly based on heuristic or greedy approaches. This study presents the malatya vertex-cover algorithm, which provides an efficient solution and a robust approach based on the malatya centrality value algorithm for MVCP. Although MVCP is an NP-complete problem that cannot be solved in polynomial time, the proposed method offers a polynomial solution to this problem, and the obtained solutions are optimum or near-optimum (optimal solution). This algorithm consists of two basic steps. In the first step, the malatya centrality values of the nodes in the graph are calculated using the malatya centrality algorithm. The malatya centrality value of the nodes in any graph is the summation of the ratio of the node's degree to the adjacent nodes' degrees for each node. In the second step, nodes are selected for the MVCP solution based on the node with the maximum malatya centrality value (psi) in the graph is selected and added to the solution set. Then this node and the edges incident on this node are removed from the graph. For the graph consisting of the remaining nodes, malatya centrality values are calculated again, and the selection process is continued. The process is terminated when all edges in the graph are covered. The proposed algorithm has been tested on artificial, actual graphs and large-scale random graphs produced with the Erdos-Renyi model. When the result

关键词： Minimum vertex-cover Graph theory malatya centrality algorithm malatya vertex-cover algorithm centrality algorithm

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